If Earth shrinks to half its radius keeping mass constant, the new esc…

Question

If Earth shrinks to half its radius keeping mass constant, the new escape velocity becomes:

Accepted Answer

A. √2 times original

v_esc = √(2GM/R).
**If R becomes R/2 with M constant:** v'_esc = √(2GM/(R/2)) = √2 × √(2GM/R) = √2 × v_esc.
**So escape velocity increases by factor √2.**

Answer

Half

Answer

Twice

Answer

Same as before

If Earth shrinks to half its radius keeping mass constant, the new escape velocity becomes:

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